1. Field of the Invention
The present invention relates broadly to a method and system for producing a sequence approximating a series of sample values. The sample value series may be never-ending. The present invention will be described herein with reference to a method and system for producing a 1-bit sequence from samples of an input waveform.
2. Background of the Invention
The present invention has been developed after extensive studies in the field of Sigma-Delta modulation. Sigma-delta modulators are normally utilized to convert analog signals to sequences of corresponding 1-bit values such that the filtering of such a 1-bit sequence by a low pass filter results in a reproduction of the original analog signal or a close version thereof. For a background description of the operation of 1-bit sigma-delta modulators, reference is made to standard textbooks in the field such as “Delta-Sigma Data Converters, Theory Design and Simulation” by Norsworthy, et al., IEEE press, 1997.
More specifically, the accurate approximation of an analog input signal by a sequence of 1-bit values wherein the bits take on the usual +1 and −1 values was initially investigated. The design being such that upon filtering of the sequence of 1-bit values, a close approximation of the original analog signal is returned.
Turning now to FIG. 1-4, there is illustrated an example of the steps in a normal 1-bit conversion process. In FIG. 1, there is illustrated an example input waveform 10, with a maximum amplitude that is no greater than +/−P. The normal conversion process involves sampling the waveform of FIG. 1 at predetermined points in time separated by a time interval so as to produce a series of sample values, e.g., 12 as illustrated in FIG. 2. Next, the core process of converting the sample values to corresponding +1 and −1 values is illustrated in FIG. 3 with a sample value illustrated, e.g., 14. Subsequently, as illustrated in FIG. 4, a one-bit output stream is output 16 corresponding to the set of sample values determined in FIG. 3. The determination of the sample values can proceed by many prior art methods. The preferred embodiment of the present invention is directed to the creation of an improved determination method which produces lower relative levels of noise than that provided by prior art methods.
The maximum input signal amplitude relative to the maximum output signal amplitude, (P) must typically be less than 1, and in practice, most techniques used to produce one-bit output streams will require that P is no greater than approximately 0.5. A further preferred embodiment of the present invention is directed to the generation of one-bit sequences wherein the maximum signal level (P) may be significantly greater than 0.5, with typical values as high as 0.75 being achievable, without a significant reduction of Signal to Noise Ratio (SNR).